5.14 Differential equations: separation of variables Quiz

1. A population $P$ decreases at a rate proportional to $P$. Which equation models this, with $k>0$?

• A. $\frac{dP}{dt}=-kP$
• B. $\frac{dP}{dt}=kP$
• C. $\frac{dP}{dt}=-kt$
• D. $\frac{dP}{dt}=\frac{k}{P}$

2. Find the general solution of $\frac{dy}{dx}=3y$.

• A. $y=3x+A$
• B. $y=Ae^{x}$
• C. $y=Ae^{3x}$
• D. $y=3Ae^{x}$

3. $\frac{dy}{dx}=2y$ and $y=5$ when $x=0$. Find $y$ when $x=1$.

• A. $13.6$
• B. $36.9$
• C. $10$
• D. $7.39$

4. What name is given to a solution that still contains an arbitrary constant?

• A. Particular solution
• B. Equilibrium solution
• C. Exact solution
• D. General solution

5. A tank drains with $\frac{dV}{dt}=-0.2V$, where $t$ is in minutes. How long does it take for $V$ to halve?

• A. $2.50$ minutes
• B. $5.00$ minutes
• C. $3.47$ minutes
• D. $0.139$ minutes